theorem :: SIN_COS9:93

for Z being open Subset of REAL st Z c= dom ((1 / 2) (#) ((#Z 2) * arctan)) & Z c= ].(- 1),1.[ holds
( (1 / 2) (#) ((#Z 2) * arctan) is_differentiable_on Z & ( for x being Real st x in Z holds
(((1 / 2) (#) ((#Z 2) * arctan)) `| Z) . x = (arctan . x) / (1 + (x ^2)) ) )